Comparison between specialized quadrature rules for method of moments with NURBS modelling applied to periodic multilayer structures
Authors
Florencio Díaz, Rafael; Somolinos Yagüe, Álvaro; González Diego, Iván; Cátedra Pérez, Manuel Felipe; Lozano Plata, LorenaIdentifiers
Permanent link (URI): http://hdl.handle.net/10017/60190DOI: 10.3390/electronics9122043
ISSN: 2079-9292
Publisher
MDPI
Date
2020-12-02Affiliation
Universidad de Alcalá. Departamento de Ciencias de la Computación; Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente MatemáticasFunders
Agencia Estatal de Investigación
Junta de Comunidades de Castilla-La Mancha
Bibliographic citation
Florencio Díaz, R., Somolinos Yagüe, Á., González Diego, I., Cátedra Pérez, M.F. & Lozano Plata, L. 2020, "Comparison between specialized quadrature rules for method of moments with NURBS modelling applied to periodic multilayer structures", Electronics, vol. 9, no. 12, art. no. 2043, pp. 1-14.
Keywords
Integral equations
Moment methods
Multilayered media
Periodic structures
Reflectarrays
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TEC2017-89456-R/ES/AVANCE EN LA SOLUCION DE PROBLEMAS ELECTROMAGNETICOS MULTIESCALA/
info:eu-repo/grantAgreement/JCCM//SBPLY%2F17%2F180501%2F000433
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.3390/electronics9122043Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2020 The authors
Access rights
info:eu-repo/semantics/openAccess
Abstract
A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.
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